-Let Them Eat Cake -
Ye Olde FoodKing, a regional food marketer has retained you to forecast the demand for small cakes that are mass-produced and marketed under the name Big Suzy s Snack Cakes. To assist with your analysis, you are provided with data that was collected for 8 consecutive quarters and 6 geographic markets.After reviewing the data, you decide the best approach is to estimate a regression model to forecast the demand for their product. Based on your knowledge of economic theory, you estimate the model with quantity of pies sold as a function of your price, your competitors price, per capita income in each market, and the population of each market.
As you present your initial results to a management team from Ye Olde FoodKing, they begin to -pepper- you with questions.
Mr. Alpha: -Looking at the data, I see that the amount ofpies we sell varies from market to market and quarter to quarter. How good is your model at explaining that variation? Is there any way to measure how much ofthat variation is explained? -
Ms. Beta: -Well you model might help us predictfor this dataset, but when I took statistics in no, MBA program, they told us to make sure the Inodel is statistically significant — usually at the 5% level. Is your model significant at that level? I know what Mr. Alpha asked, but does your answer to him guarantee significance for me? -
Mr. Cappa: -Well, Ive been around the block before and all this math doesn t mean anything unless you can explain it to me in -plain English. - I see you underlined that coefficient on price? In -plain English - what does that coefficient ntean? How do we know that price does help explain the number of cakes I sold?
Ms. Beta: and is it significant or does itjustfit this data set?
Mr. Alpha: -Okay, but - Ive always thought that our customer s inconte really drove sales. I ntean, it looked to me like we never sold as Inany pies in less qffluent markets. Is that true? Does your ntodel help us understand that?
Ms. Beta: . and is the -income effect- significant?
Mr. Cappa: Our EVP has been talking about expanding into new market. In this ntar/cei; the population is 2; 550, the average income is $41 , 500 and the contpetitor s product sells for $4.75. Based on your ntodel, ifwe price our product at $5.25, how many cakes will we sell?
Ms. Beta: In my _MBA program, we always talk about whether demand was elastic or inelastic. Ifwe price our product at $5.25, what would be the rice elastici o demandfor our product at that price? Is this elastic or inelastic?
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Mr. Cappa: Forget all that elasticity stuff— that won t be of any help. What I need to know is ifI am pricing the product right. Ifwe raised the price of the product by a very small amount, would the puofit rise orfall? That is all I need to /oaow.
Ms. Beta: Well, it may turn out that elasticity helps us understand that. But we may need to know something about cost before we can figure out if the profit rises or fall? Is that the case — do you need to know anything about our cost before you can answer Mr. Cappa?
Mr. Alpha: Enough with that elasticity junk. Just tell me this - at what price do we maximize total revenue?
Ms. Beta: Yes, and what is our price elasticity at that price?
Mr. Cappa: You marketingfolks always talk about revenue, Forget revenue, profits are what matter. What us finance guys want to know is — at know what price do we maximize profits?
Ms. Beta: I think we will have to tell him the incremental cost of our pies for him to answer?
Mr. Cappa: Okay, its $2.25 per pie now, whats the answer?
Ms. Beta: Yes, and what is our price elasticity at that price?
Mr. Alpha: Do you remember last year? We had that other consultant who suggested that there is a seasonal pattern in the data. Specifically, she said that pie sales may be higher during the fourth quarter because of the holidays. Is that true?
Ms. Beta: . and how would you testfor that? And do we know if that effect is significant?
Mr. Cappa: Yeah, and while we are at it, the new market that the E VP wants us to enter is located in the southern part of the nation and everyone knows that -Southerners eat lots ofsnack cakes. - It looks like you have two southern cities in your dataset, Atlanta and Dallas. Can you test to see ifwhat they say about Southerners is true?
Ms. Beta: and do we know if that effect is significant?
Since the management team hit you with so many questions, they asked you to return the following day with answers to all the questions.. Armed with your data and your trusty laptop (which is loaded with a spreadsheet tool has regression and optimization capabilities), how would you address their questions?
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